無年度 - 主題課程_向量空間：向量空間和子空間#107951

Which of the following is a vector space?
(A) P={p|p is a polynomial in of any order}
(B)={p|pis a polynomial in of exactly th order}

(C){T| T： is a linear transformation}

(D) The set of all matrices of which the sum of all entries is zero, i.e., .
(E) The set of all square matrices with trace 1 , i.e., .

Let vectors x ∈ be represented as x = . Which of the following sets is a subspace
of ?
(A)
(B)
(C) for some known constants ∈ R.

(D), where n is assumed to be even in this case.
(E) , where n is assumed to be even in this case.